Highest Common Factor of 234, 862, 621 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 234, 862, 621 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 234, 862, 621 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 234, 862, 621 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 234, 862, 621 is 1.

HCF(234, 862, 621) = 1

HCF of 234, 862, 621 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 234, 862, 621 is 1.

Highest Common Factor of 234,862,621 using Euclid's algorithm

Highest Common Factor of 234,862,621 is 1

Step 1: Since 862 > 234, we apply the division lemma to 862 and 234, to get

862 = 234 x 3 + 160

Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 160 and 234, to get

234 = 160 x 1 + 74

Step 3: We consider the new divisor 160 and the new remainder 74, and apply the division lemma to get

160 = 74 x 2 + 12

We consider the new divisor 74 and the new remainder 12,and apply the division lemma to get

74 = 12 x 6 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 234 and 862 is 2

Notice that 2 = HCF(12,2) = HCF(74,12) = HCF(160,74) = HCF(234,160) = HCF(862,234) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 621 > 2, we apply the division lemma to 621 and 2, to get

621 = 2 x 310 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 621 is 1

Notice that 1 = HCF(2,1) = HCF(621,2) .

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Frequently Asked Questions on HCF of 234, 862, 621 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 234, 862, 621?

Answer: HCF of 234, 862, 621 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 234, 862, 621 using Euclid's Algorithm?

Answer: For arbitrary numbers 234, 862, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.